Question

cine ne poate ajuta?
trebiie demonstrat ca a si b sunt patrate perfecte

Answer 1

[tex] 3^{2k+3}* 4^{3+2k}- 2^{2k+1}* 6^{2k+3} \\ =3^{2k+3} * 2^{2(3+2k)} - 2^{2k+1} * (2*3)^{2k+3} \\ = 3^{2k+3} * 2^{2(3+2k)} - 2^{2k+1} * 2^{2k+3} * 3^{2k+3} \\=3^{2k+3} * 2^{2k+3} ( 2^{2k+3} - 2^{2k+1} ) \\ = 6^{2k+3} ( 2^{2k} * 2^{3} - 2^{2k} *2) \\ = 6^{2k+3} * 2^{2k} ( 2^{3} -2) \\ = 6^{2k+3}* 6*2^{2k} \\ = 6^{2k+4} * 2^{2k} \\ = 6^{2(k+2)} * 2^{2k} \\ = (6^{ k+2})^{2} } *(2^{ k})^{2} } \\ = (6^{ k+2}* {2} ^{k})^{2} \\ q.e.d.[/tex]